Lattice Boltzmann modeling of complex fluids: Colloidal suspensions and fluid mixtures

The study of complex fluid dynamics requires development of numerical tools that capture the essentials of the dynamic coupling among the different particles that characterize these materials. At the same time these techniques should operate on mesoscopic time and length scales, such that the relevant phenomena can be addressed in detail. Lattice Boltzmann (LB) is a simulation procedure that, although initially introduced to address problems related to fluid flows at high Reynolds numbers, has proven to be a very flexible technique to study complex fluids in generic geometries. I will address the fundamentals of the method and describe in detail two different perspectives to model complex fluids: Colloidal suspensions, where the mesoscopic particles are described in full detail, and non-ideal fluid mixtures, where there exists no clear length scale separation. In this case, a coarse-grained description of the interactions is enough to capture the essentials of the collective dynamics. In both cases I analyze the basic formulation, emphasizing their similarities, and I will afterward discuss new results that have been obtained using LB in these systems.